|材料类型：||文献, 硕士论文/博士论文, 互联网资源|
Jeffrey Edward Danciger; Steve Kerckhoff; G Carlsson; Maryam Mirzakhani; Stanford University. Department of Mathematics.
|注意：||Submitted to the Department of Mathematics.|
|描述：||1 online resource|
We introduce a geometric transition between two homogeneous three-dimensional geometries: hyperbolic geometry and anti de Sitter (AdS) geometry. Given a path of three-dimensional hyperbolic structures that collapse down onto a hyperbolic plane, we describe a method for constructing a natural continuation of this path into AdS structures. In particular, when hyperbolic cone manifolds collapse, the AdS manifolds generated on the "other side" of the transition have tachyon singularities. The method involves the study of a new transitional geometry called half-pipe geometry. We also discuss combinatorial/algebraic tools for constructing transitions using ideal tetrahedra. Using these tools we prove that transitions can always be constructed when the underlying manifold is a punctured torus bundle.